在 R 中拟合瑞利

Question

此代码

library(ggplot2)
library(MASS)
# Generate gamma rvs
x <- rgamma(100000, shape = 2, rate = 0.2)
den <- density(x)
dat <- data.frame(x = den$x, y = den$y)

ggplot(data = dat, aes(x = x, y = y)) + 
  geom_point(size = 3) +
  theme_classic()


# Fit parameters (to avoid errors, set lower bounds to zero)

fit.params <- fitdistr(estimate, "gamma", lower = c(0, 0))

# Plot using density points

ggplot(data = dat, aes(x = x,y = y)) + 
  geom_point(size = 3) +     
  geom_line(aes(x=dat$x, y=dgamma(dat$x,fit.params$estimate["shape"], fit.params$estimate["rate"])), 
color="red", size = 1) + 
  theme_classic()

拟合并绘制序列 x 的分布。结果图是：包 stats 和 MASS 似乎不支持瑞利分布。如何将前面的代码扩展到瑞利分布？

Answer 1

在下面的代码中，我首先重新创建向量 x，这次设置 RNG 种子，以使结果可重现。然后 data.frame dat 也将重新创建仅包含该向量的

Gamma 和 Rayleigh 分布的密度函数通过首先估计它们的参数并使用 stat_function.

拟合 x 的直方图

library(ggplot2)
library(MASS)
library(extraDistr)  # for the Rayleigh distribution functions

# Generate gamma rvs
set.seed(2020)
x <- rgamma(100000, shape = 2, rate = 0.2)
dat <- data.frame(x)

# Fit parameters (to avoid errors, set lower bounds to zero)
fit.params <- fitdistr(dat$x, "gamma", lower = c(0, 0))

ggplot(data = dat, aes(x = x)) + 
  geom_histogram(aes(y = ..density..), bins = nclass.Sturges(x)) +
  stat_function(fun = dgamma,
                args = list(shape = fit.params$estimate["shape"], 
                            rate = fit.params$estimate["rate"]), 
                color = "red", size = 1) + 
  ggtitle("Gamma density") +
  theme_classic()


fit.params.2 <- fitdistrplus::fitdist(dat$x, "rayleigh", start = list(sigma = 1))
fit.params.2$estimate

ggplot(data = dat, aes(x = x)) + 
  geom_histogram(aes(y = ..density..), bins = nclass.Sturges(x)) +
  stat_function(fun = drayleigh,
                args = list(sigma = fit.params.2$estimate), 
                color = "blue", size = 1) + 
  ggtitle("Rayleigh density") +
  theme_classic()

要绘制问题中的点和线，而不是直方图，请使用下面的代码。

den <- density(x)
orig <- data.frame(x = den$x, y = den$y)

ggplot(data = orig, aes(x = x)) + 
  geom_point(aes(y = y), size = 3) +     
  geom_line(aes(y = dgamma(x, fit.params$estimate["shape"], fit.params$estimate["rate"])), 
            color="red", size = 1) + 
  geom_line(aes(y = drayleigh(x, fit.params.2$estimate)), 
            color="blue", size = 1) + 
  theme_classic()

在 R 中拟合瑞利

Fitting Rayleigh in R

r

curve-fitting